I do not understand even your first equation. It looks like a sum of moments about left hand end equals zero. But there will be an angular acceleration here, and the system has a moment of inertia about that axis.
About what point does it not have any MoI?

I do not understand even your first equation. It looks like a sum of moments about left hand end equals zero. But there will be an angular acceleration here, and the system has a moment of inertia about that axis.
About what point does it not have any MoI?

Yes I used the sum of moments. Actually I also havent get the point of this problem. Just think that it will be balance like that

OK, but the standard equation, relative to a specified axis, is Σmoment=MoI * angular acceleration. The bar will in general have an angular acceleration, and the MoI of the bar+mass about the ends of the bar is not zero. So the sum of the moments will not be zero.
As I asked before, about what axis does the bar+mass have zero MoI?